Fig. 2

Autocorrelations of gene expression levels in close chromosomal proximity and illustration of the utilized Hidden Markov Model for decoding of gene expression states. A, Autocorrelations in the chromosomal order of genes (red) are significantly greater than the autocorrelations of 1000 randomly permuted gene expression profiles (black). The autocorrelation was calculated chromosome-wise and weighted according to the number of genes on the chromosome. Decreasing autocorrelations of log\(_2\)-expression-ratios between intra- and extracranial metastases of genes in chromosomal order with increasing lag between the genes show that chromosomal distant genes have less similar expression than genes that are closer to each other on a chromosome. The yellow ribbon shows the standard deviations of the observed autocorrelations. B, Illustration of the three-state Hidden Markov Model (HMM) with state-specific Gaussian emission densities that was used to perform the personalized analysis of the patient-matched metastasis pairs. Genes with unchanged expression in the intra- compared to the corresponding extracranial metastasis are assigned to the state ’\(=\)’, genes with decreased expression in the intra- compared to the extracranial metastasis are assigned to the state ’−’, and genes with increased expression in the intra- compared to the extracranial metastasis are assigned to the state ’\(+\)’. The arrows that connect the states represent possible state transitions for directly neighboring genes on a chromosome and the corresponding values represent the learned state transition probabilities